Problem $1\mathrm{.}1$:

Consider solution of the tapered axially loaded bar shown. Divide the bar into two finite elements and determine the axial force distribution in the bar. Plot this force distribution. Compute the support reactions from the force distribution and see whether the overall equilibrium is satisfied. Comment on the quality of the finite element solution.

$($a$)$ Use two linear elements.

$($b$)$ Use two quadratic elements.

Use the following numerical data: $E=70$GPa,$F=20kN,L=300mm,A_1=2400m{m}^2,A_2=600m{m}^2$